Given the fact that the TYPO3 site is now working again, is clean and
that the security hole has been identified and fixed, you can switch
the website back online. However, there are some further things to do
or to consider:

change (all) passwords and other access details

review situation: determine impact of the attack and degree of damage

possibly notify your hosting provider

possibly notify users (maybe clients), business partners, etc.

possibly take further legal steps (or ask for legal advice from
professionals)

Depending on the nature of the hack, the consequences can be as
minimal as a beautifully “decorated” home page or as extensive as
stolen email addresses, passwords, names, addresses and credit card
details of users. In most cases, you should definitely not trifle with
your reputation and you should not conceal the fact that your site has
been hacked.